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This article presents the results of a qualitative research, in which the objective was to investigate what knowledge is produced by future mathematics teachers, in mathematical, methodological, technological aspects and on the approach of socially relevant issues, through design, (re ) formulation and resolution of open problems and the planning and implementation of pedagogical practices, in which said problems are proposed. To achieve this, three students, in a group, carried out the activities of an extension course, which allowed them to acquire experiences, and which contributed to the production of teaching knowledge related to the design of open problems and that address topics of social relevance, with the use of digital technologies and on the planning and implementation of pedagogical practices, in which the (re) formulation and resolution of these problems is evident.
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